BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Xavier Tolsa (ICREA - Universitat Autònoma de Barcelona - CRM) DTSTART:20220705T160000Z DTEND:20220705T170000Z DTSTAMP:20260423T021000Z UID:OSGA/117 DESCRIPTION:Title: T he regularity problem for the Laplace equation and boundary Poincaré ineq ualities in rough domains\nby Xavier Tolsa (ICREA - Universitat Autòn oma de Barcelona - CRM) as part of Online Seminar "Geometric Analysis"\n\n \nAbstract\nGiven a bounded domain $\\Omega \\subset \\mathbb R^n$\, one s ays that the\n$L^p$-regularity problem is solvable for the Laplace equatio n in $\\Omega$\nif\, given any continuous function $f$ defined in $\\parti al \\Omega$ and the\nharmonic extension $u$ of $f$ to $\\Omega$\, the non- tangential maximal\nfunction of the gradient of $u$ can be controlled in $ L^p$ norm by the\ntangential derivative of $f$ in $\\partial\\Omega$. Up t o quite recently this\nwas only known to hold for Lipschitz domains (in so me range of $p$'s). \nIn my talk I will explain a recent result with Mihal is Mourgoglou where we\nshow that the $L^p$-regularity is also solvable in more general domains\,\nsuch as 2-sided chord-arc domains. In the solutio n of this problem\, the\nPoincaré inequality in the boundary of the domai n plays an important role. I\nwill also discuss this issue and a related j oint result with Olli Tapiola\nwhere we show that the boundaries of 2-side d chord-arc domains support\n1-Poincaré inequalities.\n LOCATION:https://researchseminars.org/talk/OSGA/117/ END:VEVENT END:VCALENDAR